T3: Superfluidity in Strong Dipolar Quantum Gases

Within the first period, the Research Unit has been successful in determining the properties of ultracold large magnetic lanthanides, such as dysprosium and erbium, and has achieved substantial progress towards realizing heteronuclear molecules in the quantum degenerate regime. Therefore, in the second period, this new project will theoretically analyze the emergence of superfluidity for strong dipolar quantum gases, which represents a hallmark of quantum many-body physics.

One focus will be on studying dipolar fermions in a harmonic confinement, where the Fermi sphere has already been shown to be deformed into an ellipsoid, which follows the orientation of the dipoles. At first, we will investigate to which degree also the spatial distribution is rotated towards the dipolar preference direction. This will allow us to study how the critical dipolar strength, up to which the Fermi gas could be confined, depends on the interplay of trap geometry and dipolar orientation. Then we will investigate for such a general geometry dynamical aspects, like non ballistic time-of-flight or collective excitations, all the way from the collisionless to the hydrodynamic regime. In particular, we will explore whether a periodic modulation of the harmonic confinement could enhance the ellipsoidal deformation of the Fermi sphere due to parametric resonance. Based on these results we will then come to the major question how the superfluid pairing in a single-component dipolar Fermi gas, which has been predicted some time ago, is modified by the deformation of the Fermi sphere. Here it is of interest to study how the emergent superfluidity as well as its anisotropic order parameter and its critical temperature can be tuned by both the trap geometry and the dipolar orientation.

In addition, we will also join the quest of the Research Unit for a better understanding of the anisotropic superfluid properties of dipolar quantum droplets, which arise in a strong dipolar Bose gas. On the one hand, we will investigate how quantum and thermal fluctuations affect the stability of dipolar quantum droplets and their anisotropic velocity of sound. On the other hand, we will be interested in the emergence of quantum droplets in fast-rotating dipolar Bose-Einstein condensates and consider whether the presence of vortices in the system enhances this process. Here we will explore if it is possible to generate quantum droplets with angular momentum using this protocol and study how this affects both the formation and the shape of the droplet crystals, as well as their phase coherence.